2c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

The third part of this standard is all about switching between proportions and equations. This one's pretty self-explanatory—the trick here is to identify the right dependent variable.

For example, if there are 5 breadcrumbs for each duck, students should know to express this relationship as b = 5d. Verbal descriptions like this one can be a little tricky, though—it might be tempting to follow the order of the sentence and write "5 breadcrumbs per duck" as 5b = d. Help them out by explaining how the dependent variable always goes on the left side of the equation by itself, with the constant of proportionality and the independent variable on the right.

In this case, the number of breadcrumbs depends on the number of ducks, so the total amount of breadcrumbs will be 5 per duck (b = 5d). Bringing any less than that to the pond would just be insulting to duck-kind.